Binary prefix

The binary prefixes are used to create binary multiples, that is, base 2 (binary system). They are currently part of the international standard ISO/IEC 80000-13.

Overview

They are normally used to create multiples of the byte, being similar in concept to the SI prefixes, although these are base 10 (decimal system), which can lead to serious confusion, since the resulting values are different, for example:

• 1 kibibyte = 1024 bytes = 2¹⁰ bytes. ISO/IEC 80,000-13 binary prefix.
• 1 kilobyte = 1000 bytes = 10³ bytes. IF Prefix.

1. At the time of 32 KB memory computers ROM this difference was relatively small, as the difference between 2¹⁰ and 10³ It's 2.4%. On the other hand, with the rapid growth of the capacity of memories and storage peripherals today, differences lead to increasing errors. (See Table of Differences)

Linux/GNU

The binary prefixes []-13 are already used by some GNU/Linux distributions, for example: However, GNU Coreutils, available from terminals like Bash, uses the ls command, which uses powers of 1024 denoted as KB /MB.

History

IEC 60027-2

To end the confusion caused by the use of two different interpretations for binary prefixes, in February 1999 the IEC technical committee 25 (quantities and units) published IEC 60027-2:

In this rule, introduce the prefixes kibi, mebi, gibi, tebi, pebi and exbi, names formed with the first two letters of each SI prefix and the suffix bi for binary. The standard also stipulates that SI prefixes will always have the values of powers of 10 and should never be used as powers of 2. In 2005 the IEC published the third revision of the standard, adding the prefixes, zebi and yobi.

Eighth edition of the SI

The eighth edition of the International System of Units (SI) published in 2006 specifies that SI prefixes are used strictly to refer to powers of 10, and recommends that the prefixes adopted by the IEC for binary powers in the standard international IEC 60027-2:2005, third edition are used in the field of information technology to prevent the incorrect use of SI prefixes, even though these prefixes are not part of the SI.

ISO/IEC 80000-13

ISO/IEC 80000-13 is a revised and harmonized standard resulting from ISO 31 and IEC 60027, incorporating the IEC binary prefixes. (See Table ISO/IEC 80000-13 (in bytes))

Related Standards

IEEE 1541-2002

The IEEE accepted the use of binary prefixes for its members under IEEE 1541-2002 published in 2002 and elevated to a standard in 2005. The standard, later a standard, was closely related to the IEC standard 60027-2, but with the difference that the latter used the symbol bit for the bit.

Misuse of SI prefixes

Prior to the international standard ISO/IEC 80000-13, the SI prefixes were used to determine both base 2 (Binary System) and base 10 (Decimal System) values, which is not possible, since 1000 does not is 1024.

Telecommunications

Telecommunications engineers commonly use and used SI prefixes to determine base 2 values (binary system). Although differently, since they use bits, not bytes. For example:

• In a connection of 1 Mbit/s, the data transferred is 1 000 000 bit/s. Which are actually: 125 000 B/s or 125 kB/s.

Storage device manufacturers

Manufacturers of data storage devices routinely use and use SI prefixes to determine base 2 values (Binary System), contributing to the confusion.

When purchasing a storage device (such as a hard drive) you often find that the manufacturer gives the device's storage capacity using SI prefixes, but the computer returns the data with ISO/IEC 80000 binary prefixes -13.

Formula

To convert the figure from base 10 (decimal system) to base 2 (binary system) format, the following formula must be followed, where N is the data that the manufacturer will give you in SI prefixes and R the data with ISO/IEC 80000-13 binary prefix, which is to be found.

N↓ ↓ 10x2and=R{displaystyle {{N*10^{x} over 2^{y}}=R}

Changing the exponent x by SI powers. For example giga (G)= 10⁹, that is, x is equal to 9.

Changing the exponent y to powers from ISO/IEC 80000-13. For example gibi (Gi) = 2³⁰, that is, y is equal to 30.

(See the table at the top of this article to get the exponents x and y quickly.)

Example

A 500 gigabyte (GB) hard drive.

500↓ ↓ 109230=R=465,661287≈ ≈ 465{displaystyle {{500*10^{9} over 2^{30}}=R=465,661287approx 465}

So the capacity expressed with ISO/IEC 80000-13 binary prefix will be 465 gibibytes (GiB) (decimal places should be ignored). When connecting the hard disk to the computer, it is verified that it indeed indicates the amount available as 465 gibibytes (GiB) (or 465 gigabytes (GB) if the operating system incorrectly uses the SI prefixes as multiples of 1024).

• It should be taken into account that:

1. The capacity expressed with decimal prefix results in a higher number than if expressed with binary prefix.
2. The higher capacity has a hard drive, the greater the difference between the figures that express this ability with decimal or binary prefix.

Floppy Disk Manufacturers

Floppy disk manufacturers worked in a totally different way, for them the prefix mega (symbol M) did not mean (1000 x 1000) = 1 000 000 (10 ⁶) bytes. Nor did they use (1024 x 1024) 1 048 576 (2²⁰) bytes, like the ISO/IEC 80000-13 standard.

For example:

• The common diskette of 1.44 MB had a capacity of (1.44 × 1000 × 1024) = 1 474 560 bytes.

Tables

ISO/IEC 80000-13 Tables

1. The bit symbol in the ISO/IEC 80000-13 standard is bit and is always written in tiny. (See References)
2. Values are in bit, there is no confusion with byte.
3. To make a bit to byte conversion, divide the amount of bits between 8. Example:
   * 1 048 576 mebibit = 1 048 576 / 8 mebibyte = 131 072 mebibyte.

Differences table